Delta-Davidson method for interior eigenproblem in many-spin systems

TL;DR

The paper introduces the DELDAV method, combining Delta filtering and Chebyshev expansion, to efficiently compute interior eigenstates in many-spin quantum systems, addressing challenges of near-degeneracy.

Contribution

It presents a novel Delta-Davidson approach that effectively finds interior states in many-spin systems, a problem less explored compared to ground state calculations.

Findings

Successfully computes interior states in Ising spin chains and spin glasses.

Demonstrates robustness and efficiency in handling nearly degenerate states.

Potential applications in identifying many-body localization and quantum chaos.

Abstract

Many numerical methods, such as tensor network approaches including density matrix renormalization group calculations, have been developed to calculate the extreme/ground states of quantum many-body systems. However, little attention has been paid to the central states, which are exponentially close to each other in terms of system size. We propose a Delta-Davidson (DELDAV) method to effciently find such interior (including the central) states in many-spin systems. The DELDAV method utilizes Delta filter in Chebyshev polynomial expansion combined with subspace diagonalization to overcome the nearly degenerate problem. Numerical experiments on Ising spin chain and spin glass shards show the correctness, effciency, and robustness of the proposed method in finding the interior states as well as the ground states. The sought interior states may be employed to identify many-body localization phase, quantum chaos, and extremely long-time dynamical structure.